# Properties

 Base field 5.5.160801.1 Weight [2, 2, 2, 2, 2] Level norm 9 Level $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ Label 5.5.160801.1-9.2-d Dimension 7 CM no Base change no

# Related objects

• L-function not available

## Base field 5.5.160801.1

Generator $$w$$, with minimal polynomial $$x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2, 2] Level $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ Label 5.5.160801.1-9.2-d Dimension 7 Is CM no Is base change no Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{7}$$ $$\mathstrut -\mathstrut 13x^{5}$$ $$\mathstrut -\mathstrut 3x^{4}$$ $$\mathstrut +\mathstrut 35x^{3}$$ $$\mathstrut -\mathstrut 4x^{2}$$ $$\mathstrut -\mathstrut 13x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-\frac{2}{3}e^{5} + \frac{1}{3}e^{4} + \frac{20}{3}e^{3} + \frac{4}{3}e^{2} - \frac{26}{3}e - \frac{7}{3}$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-\frac{4}{3}e^{6} + \frac{1}{3}e^{5} + 16e^{4} + 2e^{3} - \frac{110}{3}e^{2} + 5e + \frac{22}{3}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-\frac{2}{3}e^{6} + \frac{22}{3}e^{4} + \frac{11}{3}e^{3} - 12e^{2} - \frac{8}{3}e + \frac{10}{3}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $-\frac{1}{3}e^{6} + \frac{1}{3}e^{5} + 4e^{4} - 2e^{3} - \frac{29}{3}e^{2} + 3e - \frac{2}{3}$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{1}{3}e^{6} + \frac{1}{3}e^{5} - \frac{16}{3}e^{4} - \frac{8}{3}e^{3} + \frac{52}{3}e^{2} - \frac{19}{3}e - 6$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{2}{3}e^{6} - \frac{31}{3}e^{4} + \frac{4}{3}e^{3} + 36e^{2} - \frac{58}{3}e - \frac{31}{3}$
32 $[32, 2, 2]$ $\phantom{-}\frac{1}{3}e^{6} - \frac{14}{3}e^{4} - \frac{4}{3}e^{3} + 14e^{2} + \frac{10}{3}e - \frac{14}{3}$
37 $[37, 37, w^{3} - 3w - 1]$ $-\frac{1}{3}e^{6} + e^{5} + \frac{8}{3}e^{4} - \frac{23}{3}e^{3} - 3e^{2} + \frac{32}{3}e + \frac{8}{3}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-\frac{5}{3}e^{6} - \frac{2}{3}e^{5} + \frac{68}{3}e^{4} + \frac{28}{3}e^{3} - \frac{182}{3}e^{2} + \frac{32}{3}e + 14$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-\frac{4}{3}e^{6} - \frac{4}{3}e^{5} + \frac{52}{3}e^{4} + \frac{53}{3}e^{3} - \frac{112}{3}e^{2} - \frac{29}{3}e + 4$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $\phantom{-}e^{6} - 12e^{4} - 4e^{3} + 25e^{2} - 4$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-2e^{6} - e^{5} + 24e^{4} + 19e^{3} - 48e^{2} - 13e + 8$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-\frac{1}{3}e^{6} - e^{5} + \frac{17}{3}e^{4} + \frac{25}{3}e^{3} - 15e^{2} + \frac{11}{3}e - \frac{1}{3}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}e^{6} + \frac{1}{3}e^{5} - \frac{38}{3}e^{4} - \frac{22}{3}e^{3} + \frac{91}{3}e^{2} + \frac{7}{3}e - \frac{19}{3}$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{5}{3}e^{6} - \frac{61}{3}e^{4} - \frac{23}{3}e^{3} + 47e^{2} + \frac{11}{3}e - \frac{25}{3}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{1}{3}e^{6} + \frac{5}{3}e^{5} + \frac{10}{3}e^{4} - \frac{52}{3}e^{3} - \frac{31}{3}e^{2} + \frac{112}{3}e + 2$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $-e^{6} + \frac{5}{3}e^{5} + \frac{35}{3}e^{4} - \frac{38}{3}e^{3} - \frac{103}{3}e^{2} + \frac{59}{3}e + \frac{43}{3}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $\phantom{-}2e^{6} + \frac{1}{3}e^{5} - \frac{80}{3}e^{4} - \frac{22}{3}e^{3} + \frac{214}{3}e^{2} - \frac{47}{3}e - \frac{46}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $-1$